Hmm, if you're not using incognito I'm not sure quite what to tell you. The online version of the game stores save info in browser/cookie data from what I understand ... but I'll do some digging too and see if there's anything else I can suggest you try!
So glad to hear! I did a little more reading up, too, but yeah outside of what I suggested there wasn't much else to tell you, other than that the game seems to work better on some browsers than others. I've had success with Firefox and Safari, and I think Chrome works okay (ish) too, while Microsoft Edge is a total binfire!